Solve for x: \arctan 2x +\arctan 3x = (\frac{\pi}{4}) \arctan (\frac{2x+3x}{1-2x*3x})=\frac

occhei042

occhei042

Answered question

2022-04-22

Solve for x: arctan2x+arctan3x=(π4)
arctan(2x+3x12x3x)=π4
5x16x2=tanπ4=1
6x2+5x1=0
(6x1)(x+1)=0
x=1,16
The answer however rejects the solution x=-1 saying that it makes the L.H.S of the equation negative. I don't understand this, I don't see how x=-1 makes the L.H.S. negative.

Answer & Explanation

aimadorsozf

aimadorsozf

Beginner2022-04-23Added 10 answers

Because
arctan(2)+arctan(3)=135<0
By the way, tan(135)=1.
obettyQuokeperg6

obettyQuokeperg6

Beginner2022-04-24Added 14 answers

tan(x) is negative in the interval (π2,0) , so it's inverse on the interval (,0) will give a value from the interval (π2,0)

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